Which library would you recommend to begin with deep learning?
Keras is a simple and high-level neural networks library, written in Python, that works as a wrapper for Tensorflow and Theano. It's easy to learn and use. Using Keras is like working with Lego blocks. It was built so that people can do quick experiments and proofs-of-concept before launching into a full-scale build process. 

With that in mind, it was made to be highly modular and extensible. Now, it can be used for a lot more than just experiments. It can help with RNN, CNN, and combinations of both. 

If you want to begin and make a prototype ready solution, then I will recommend you start with Keras. To know the details under the hood, then learn TensorFlow. It has huge active community and also very good resources are available, for example, this Youtube series.

See also https://blog.keras.io/keras-as-a-simplified-interface-to-tensorflow-tutorial.html.